90 Degree Clockwise Rotation

Learn about the rules for 90 degree clockwise rotation about
the origin.

How
do you rotate a figure 90 degrees in clockwise direction on a graph?

Rotation of point through 90° about the origin
in clockwise direction when point M (h, k) is rotated about the origin O
through 90° in clockwise direction. The new position of point M (h, k) will
become M’ (k, -h).

Worked-out
examples on 90 degree clockwise rotation about the origin:

1. Plot the point
M (-2, 3) on the graph paper and rotate it through 90° in clockwise direction,
about the origin. Find the new position of M.

Solution:

When the point is rotated through 90° clockwise about the
origin, the point M (h, k) takes the image M' (k, -h).

Therefore, the new position of point M (-2, 3) will become M'
(3, 2).

2. Find the
co-ordinates of the points obtained on rotating the point given below through
90° about the origin in clockwise direction.

(i) P (5, 7)

(ii) Q (-4, -7)

(iii) R (-7, 5)

(iv) S (2, -5)

Solution:

When rotated through 90° about the origin in clockwise
direction, the new position of the above points are;

(i) The new position of point P (5, 7) will become P' (7,
-5)

(ii) The new position of point Q (-4, -7) will become Q'
(-7, 4)

(iii) The new position of point R (-7, 5) will become R' (5,
7)

(iv) The new position of point S (2, -5) will become S' (-5,
-2)

3. Construct the
image of the given figure under the rotation of 90° clockwise about the origin
O.

Therefore, P'Q'R'S' is the new position of PQRS when it is
rotated through 90°.

4. Draw a quadrilateral
PQRS joining the points P (0, 2), Q (2, -1), R (-1, -2) and S (-2, 1) on the
graph paper. Find the new position when the quadrilateral is rotated through
90° clockwise about the origin.

Solution:

Plot the point P (0, 2), Q (2, -1), R (-1, -2) and S (-2, 1)
on the graph paper. Now join PQ, QR, RS and SP to get a quadrilateral. On
rotating it through 90° about the origin in clockwise direction, the new
positions of the points are